# Relativistic Mass and Energy

If you've ever wondered if mass and energy are related, the answer is yes! They can be converted into each other using the speed of light. In physics, mass is actually a form of energy. This is because we can convert a particle's mass into different types of energy like thermal or kinetic energy. And, did you know that energy can also form particles with mass? It's true! This is because energy and mass are two sides of the same coin, linked together in a phenomenon called Relativistic Mass and Energy.

## Mass-energy conversion

There are many examples of mass-energy conversions that occur in daily life. One of them is the reason the universe exists, the Big Bang. According to the Big Bang theory, the universe was formed after a gigantic amount of energy was released and converted into mass.

In order to understand relativistic energy, we have to take into consideration total energy and rest energy.

Total energy E is the sum of all energies that an object with mass carries. Mathematically, it can be defined as:

Here, m is the mass, c is the speed of light, and y can be calculated as follows:

Here again, v is the velocity of the moving object [m/s], while c is the speed of light in a vacuum [m/s].

**Rest energy**

Rest energy refers to the energy of an object when its velocity is zero with respect to a reference frame. The rest energy of a proton can be calculated using the formula:

E0 = mc^2

where E0 is the rest energy in joules, m is the mass of the proton in kilograms, and c is the speed of light in meters per second.

Given that the mass of a proton is approximately 1.67 ⋅ 10 ^ -27 kg and the speed of light is 3.00⋅10^8m/s, we can calculate the rest energy of a single proton as:

E0 = (1.67 ⋅ 10 ^ -27 kg) x (3.00⋅10^8 m/s)^2

E0 = 1.50 x 10 ^ -10 joules

This may seem like a small amount of energy, but it is important to remember that this is only for a single proton. If we were to calculate the rest energy of one gram of mass, the result would be much larger at 9 ⋅ 10 ^ 13 J. However, we don't usually notice this energy because it is not available for use.

In summary, the rest energy of a proton can be calculated using the formula E0 = mc^2, and for a single proton, it is approximately 1.50 x 10 ^ -10 J.

## How can energy be converted into mass?

Did you know that energy can be converted into mass, just like mass can be converted into energy? To understand how this works, we need to explore the connection between stored energy and potential energy.

**Stored energy and potential energy**

The energy stored in a compressed spring is in the form of potential energy, which is converted to kinetic energy when the spring is released. This energy is also part of the total energy and mass of the spring, but the change in mass is so small that it is not noticeable in our daily lives. For example, a big battery that is able to move 700 ampere-hours (A⋅h) of charge at 15 volts has a difference in mass of only 0.000001 kg when it goes from fully discharged to fully charged. This is because the energy stored in the battery is converted to a very small amount of mass, according to the equation E = mc2[^2].

## Mass and Energy - Key takeaways

You are absolutely right! Mass and energy are two sides of the same coin, which we can convert into each other using the speed of light. The total energy of an object with mass is defined as E = ymc^2, where y is the Lorentz factor. The rest energy of an object at rest is E0 = mc^2. When there is excess energy stored, we can determine the change in mass using the equation E = PE = q⋅V = (Δm)⋅c^2. The conversion of mass into energy and vice versa is a fundamental concept in physics and has many practical applications, including the formation of the universe, nuclear power plants, and the sun.

## Relativistic Mass and Energy

**How is mass related to energy?**

Mass can be converted into energy and vice versa. The relation between mass and energy based on Einstein’s famous equation is E = mc ^ 2.

**Does the law of conservation apply to mass and energy?**

Yes, it does. When mass converts into energy or vice versa, the total energy is conserved.

**How is mass a form of energy?**

The concept that explains mass being a form of energy is rest energy. When an object has the velocity of zero, it has a rest energy that is directly proportional to its mass.